CASE STUDY CHALLENGE
Differential Equations: Camphor Sublimation
Camphor is a waxy, colourless solid with a strong aroma that evaporates through the process of sublimation if left in the open at room temperature.
A cylindrical camphor tablet whose height is equal to its radius (r) evaporates such that the rate of reduction of its volume is proportional to its total surface area. Thus:
dV / dt = kS
Where V is volume, S is surface area, and t is time in hours.
Answer the following:
| (i) | Write the order and degree of the given differential equation. | [1] |
| (ii) |
Substituting V = πr3 and S = 2πr2, we get the differential equation: dr / dt = (2/3)k Solve it, given that r(0) = 5 mm. |
[1] |
| (iii) |
(a) If it is given that r = 3 mm when t = 1 hour, find the value of k. Hence, find t for r = 0 mm. — OR —
(b) If it is given that r = 1 mm when t = 1 hour, find the value of k. Hence, find t for r = 0 mm. |
[2] |